Saponified rosin sizing agents have been employed for a long time in a so-called acidic paper-making method wherein aluminum sulfate is used. In recent years, however, regulation on environment has been tightened and thus water is repeatedly circulated in a paper making system. As a result, the temperature of the water is elevated, which seriously deteriorates the sizing efficiency of a sizing agent.
Furthermore, it is known that sizing efficiency is deteriorated under almost neutral conditions due to a decrease in the amount of aluminum sulfate.
When water temperature is elevated or only less aluminum sulfate is added in a paper-making step, as described above, it is preferable to use emulsion-type sizing agents which are superior in sizing efficiency to saponified rosin sizing agents. However these emulsion-type sizing agents have some disadvantages. Namely, they contain emulsifiers which make them highly foamable. In addition, an emulsion is broken due to a mechanical shear force and, as a result, scales and pitch are formed in pipes, tanks and paper machines. When conventional sizing agents are to be substituted with the above-mentioned emulsion-type rosin sizing agents, furthermore, it is needed to alter the equipment including a sizing agent-addition unit, which requires great expense.
On the other hand, JP-B-56-18716 discloses an improved saponified rosin sizing agent which is obtained by subjecting an addition reaction product of rosin with an .alpha.,.beta.-unsaturated acid by using a polyalkylene polyamine and saponifying a mixture of the reaction product thus obtained with rosin by using an alkali (the term "JP-B" as used herein means an "examined Japanese patent publication"). However this sizing agent cannot achieve satisfactory sizing efficiency.